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%I #11 Mar 24 2017 03:50:13
%S 0,2,2,1,35,1,2,2,1,2,5,3,1,1,45,1,1,6,11,2,9,2,2,2,2,1,1,1,29,1,3,7,
%T 4,1,7,61,1,1,2,1,2,6,2,1,1,96,11,1,2,1,1,4,14,1,10,1,2,1,7,4,7,5,10,
%U 1,6,2,2,9,6,8,3,1,3,1,3,7,9
%N Continued fraction for x value of the unique pairwise intersection on (0,1) of distinct order 5 power tower functions with parentheses inserted.
%e 0.42801103796472992390204...
%p with(numtheory):
%p f:= x-> (x^(x^x))^(x^x): g:= x-> x^(x^((x^x)^x)):
%p Digits:= 200:
%p xv:= fsolve(f(x)=g(x), x=0..0.99):
%p cfrac(evalf(xv), 120, 'quotients')[];
%t terms = 77; digits = terms+10; xv = x /. FindRoot[x^(x^2) - 2x == 0, {x, 1/2}, WorkingPrecision -> digits]; ContinuedFraction[xv, terms] (* _Jean-François Alcover_, Mar 24 2017 *)
%Y Cf. A199814 (decimal expansion), A199880 (Engel expansion).
%K nonn,cofr
%O 1,2
%A _Alois P. Heinz_, Nov 11 2011
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